name help

Stream: maths

[Johan Commelin]

Given an R-algebra homomorphism mv_polynomial I R →_a[R] mv_polynomial J R, you get an induced function (J → R) → (I → R). What is a good name for this? It is a sort of "Spec functor for dummies".

[Johan Commelin]

Should this just be mv_polynomial.comap?

[Johan Commelin]

Yup, I think it should be comap. Thanks for rubberducking!

[Chris Hughes]

I don't understand why it is comap. Usually comap is the map on homsets for contravariant functors.

[Johan Commelin]

It's contravariant in the index set of the variables.

[Chris Hughes]

What's the functor?

[Chris Hughes]

I guess it's a natural transformation

[Johan Commelin]

Normally, you have a functor from R-algebras to affine schemes over Spec(R). If R is an integral domain, there is a natural map from I → R to the spectrum of mv_polynomial I R, that sends a point x to the kernel of aeval _ _ x.

[Johan Commelin]

The spec functor is contravariant. And this comap thing is a silly approximation to Spec.

[Johan Commelin]

(It's not even getting close.)

[Johan Commelin]

But other suggestion for a name are very welcome!

[Chris Hughes]

In my mind, mv_polynomial.comap means mv_polynomial is a contravariant functor. I can't think of a better name.

[Johan Commelin]

Yeah, I agree that the name is not optimal

[Kevin Buzzard]

Maybe it's a bit like ext where there is sometimes more than one contender